Prove that if fn C[a,b], then fn f uniformly on [a, b] if and only

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Prove that if fn ∈ C[a,b], then fn → f uniformly on [a, b] if and only if fn → f in the metric of C[a, b] (see Example 10.6).

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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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Question Posted: Mar 29, 2016 04:16 AM

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Prove that if fn C[a,b], then fn f uniformly on [a, b] if and only

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a If x n E then x n is bounded Hence by the BolzanoWeierstrass Property there is an a X such ...View the full answer

An Introduction to Analysis

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